Bayesian 3x2x2 ANOVA

Our reviewers want us to do a Bayesian analysis in order to see if our results actually speak against a null-effect, or if we just have a lack of power in our measurements to detect a group difference. I find this very exciting because I have never done Bayesian statistics before and neither has any previous study asking a similar research question so I really think this could improve the field a lot!

I have read a lof of blog posts on these and I am not really able to apply them to our present issue so I thought I'd just try to post it here.

We have a memory test with three different item types that can be either neutral or negative and we have two different groups doing these tests. Thus, this is a 3 (Item Type) x 2 (Emotion) x 2 (Group) ANOVA. The regular ANOVA revealed no effects whatsoever and what I want to find out is - is this a "proper" finding revealing no group differences or interactions, or at we just not able to make anything out of these findings.

The results of the Bayesian repeated measures ANOVA looks like in the attached file.

As I said, I've been trying to read some blog posts about this but I still haven't really understood exactly how this should be interpreted. Is there anyone who has an easy way to get the BF01 for all the two-way interactions as well as for the three-way term, in a way so that they are compared to the null model?

Comments

Going by the main output table, the null seems to get most support from the data. The "only-Emo" model and "only-Villkor" models also get some support, but a factor of 4 to 5 less. All the other models seem way worse.

NB. The new JASP version (out within 10 days, I sincerely hope) will have more functionality on ANOVA, including posterior distributions on R^2, posterior distributions on the model parameters, etc.

Even though JASP provides all possible models that you could entertain, and the degree to which they are supported by the data, JASP cannot tell you which specific hypotheses you wish to test. For instance, it may be that the main effects are "nuisance factors" that you want to include into the null model, in order to focus on the potential added value of the interactions. In that case it is best to do just this (under the Model tab).